The hyperfine coupling (hfc) constants, A, and the g-factors of hydrogen isotopes confined in silasesquioxane (R8Si8O12) cages show significant deviations from the free-particle vacuum value thus revealing the influence of the environment on the wave function of the trapped atom. Accurate measurements of the hfc constants in the temperature range of 5-300 K show a strong isotope effect, different substituents on the cage corners having a clear influence on both static and dynamic cage effects. Deviations of g-factors from the free-electron value are independent of temperature, but they depend on substituents. To gain information about the factors influencing the trapped atoms' dynamic behavior inside the cage environments, a phenomenological model developed previously for the description of the dynamics of hydrogen isotopes in liquid water and ice (J. Chem. Phys. 1995, 102, 5989), which is based on the spherical harmonic oscillator, is applied to the more rigid silasesquioxane cage systems. The present study aims at a better understanding of matrix effects on the dynamics of particles in a constraining environment, a problem which represents a challenge for both phenomenological modeling and quantum chemical calculations.